I want a green for "correct answer" and a red for "wrong answer". My current choice is rgb(144, 238, 144) for the green and rgb(250, 128, 114) for the red. (See wikilearner.net/wiki for the colours in action.)

I have been told that these colors are very close in contrast, making it difficult for a person with red-green color-blindness. What would be a better choice?

it's always good practise to not simply depend singularly on colour to differentiate between states.
perhaps incorporate symbol or shape into your design.
try this very very practical tool to ensure you have enough differentiation between the two states.
http://www.vischeck.com/